For two general polytopal complexes the set of face-wise affine maps between them is shown to be a polytopal complex in an algorithmic way. The resulting algorithm for the affine hom-complex is analyzed in detail. There is also a natural tensor product of polytopal complexes, which is the left adjoint functor for Hom(-,-). This extends the corresponding facts from single polytopes, systematic study of which was initiated in [5,11]. Explicit examples of computations of the resulting structures are included. In the special case of simplicial complexes, the affine hom-complex is a functorial subcomplex of Kozlov's combinatorial hom-complex [13], which generalizes Lovasz' well-known construction [14] for graphs.

中文翻译：

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仿射同形复合体

对于两个通用的多面复合体，它们之间的一组面仿射图以算法方式显示为多面复合体。详细分析了仿射hom-complex 的结果算法。还有一个多面复形的自然张量积，它是 Hom(-,-) 的左伴随函子。这扩展了来自单个多胞体的相应事实，系统研究始于 [5,11]。包括计算结果结构的明确示例。在单纯复形的特殊情况下，仿射 hom-complex 是 Kozlov 组合 hom-复形 [13] 的函子子复形，它推广了 Lovasz 著名的图构造 [14]。